Unfortunately you don't always have the choice of keeping politics out. Activists that discover you are doing business with a company or group they disapprove of can publicize this fact, organize boycotts against you, harass your other customers, bully your employees and do everything in their power to make you go out of business if you don't cut ties with the customer which they disapprove.

The best solution for that is to still keep politics out and ignore the complainers. They only have any power at all because companies and organisations listen to them. The more people ignore angry Twitter mobs, the quicker said Twitter mobs become ineffective and people realise screaming at anything that offends them won't get them their way.